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mathslover

Prove that if the 3 altitudes of a triangle are equal then the triangle is equilateral. See attachment

  • one year ago
  • one year ago

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  1. mathslover
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    I tried to do this and have got so far that AB = AC

    • one year ago
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  2. mathslover
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    @ParthKohli

    • one year ago
  3. mathslover
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    @experimentX

    • one year ago
  4. mathslover
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    I took following triangles :ABF and AEC by AAS I got both of these triangles congruent and therefore by CPCT AB = AC

    • one year ago
  5. mathslover
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    (CPCT = Congruent Parts of Congruent Triangles are equal)

    • one year ago
  6. joemath314159
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    That idea should work to get that AB=BC as well.

    • one year ago
  7. mathslover
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    So far , we have got ABC as isosceles. Now, I took triangle ABC and AFC both of these triangles are congruent by RHS BF = FC ( by CPCT ) therefore F is mid point of BC an AF is median and altitude also Therefore , this is the property of an equilateral triangle , so ABC is an equi. triangle

    • one year ago
  8. mathslover
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    Is this correct?

    • one year ago
  9. mathslover
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    You mean to take ABE and BEC triangles @joemath314159 ?

    • one year ago
  10. joemath314159
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    yep. and do exactly what you did with the other triangles again.

    • one year ago
  11. mathslover
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    I meant this : ADC and ABD in the above comment.

    • one year ago
  12. mathslover
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    OK wait..

    • one year ago
  13. mathslover
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    I think I had tried that earlier but I didnt' get any favorable result , wait let me do it again

    • one year ago
  14. joemath314159
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    there are many combinations you could take. The pair I see is triangles BEC and BDA.

    • one year ago
  15. mathslover
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    Oh yes that will work ... BEC and BDA .. this gives some output to me.

    • one year ago
  16. mathslover
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    Thanks a lot @joemath314159 for your help .. Might gonna work in more concentration for me..

    • one year ago
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